Single-row mapping and transformation of connected graphs

In a dimensional problem, the transformation of a graph into its linear network can be viewed as a transition involving demand and supply. A connected graph represents the demand flows between the components in the graph while the network supporting it is the resource or capacity links for supporting the demand volumes. The transformation involves a mapping from the graph to its network to satisfy certain performance metrics. In this work, we propose a model for transforming a connected graph to its linear network model in the form of a single-row routing network. The main objective is to provide an optimum routing network that minimizes the congestion. In this technique, the given graph is first partitioned into several disjoint cliques using the Hopfield neural network using our model called AdCliq. From the cliques, a set of intervals derived from the zones are obtained through the matching nodes in the single-row axis. The intervals are then mapped into a network of non-crossing nets using our previously developed tool called ESSR. The network is optimal in terms of minimum street congestion and number of doglegs, and this provides a reasonably good step towards the overall solution to the demand-supply problem.     

基于图神经网络的方面级情感分析

目前基于循环神经网络和注意力机制的方面级情感分析模型缺乏解释相关句法约束和远程单词依赖关系.针对该问题提出结合句子依存树和单词序列信息建立句子关系图模型.首先将句子表示为图,单词作为图的节点,依存句法树的边和单词序列作为图的边;然后提出邻接矩阵标记方案对句子关系图进行标记;最后利用图神经网络实现节点和边的分类任务.该模型在SemEval2014任务中的restaurant和laptop两个数据集上进行实验,在两个数据集上F1值提升了5％左右.实验结果表明,将句子转换成图利用图神经网络对句子进行方面级情感分析是有益的.     

An optimal emulator and VLSI layout for complete binary trees

How complex does a graph need to be in order to emulate an arbitrary size complete binary tree with the same level of efficiency as would be obtained by a directed complete graph? In this paper, this question is answered by showing that any -node graph needs to have at least edges in order to perform this emulation. Subsequently, a graph is presented which meets this bound, and it is shown how to optimally embed an arbitrary size complete binary tree in the proposed graph. It is also shown how to optimally embed a node cycle in the proposed graph of nodes with unit dilation, unit congestion and uniform load of . Finally optimal VLSI layouts are presented for the proposed graph which require asymptotically same area as the corresponding layouts for complete binary trees. Received: 7 July 1994 / 28 May 1996     

多编码树GPU并行轴心子图匹配

子图同构问题是非确定多项式(NP)完全问题,而轴心子图同构是一种特殊的子图同构问题.针对现在已经有许多高效的子图同构算法,然而对于轴心子图同构问题目前并没有基于GPU的搜索算法,且通过改造已有的子图同构算法来解决轴心子图匹配问题会产生大量不必要的中间结果这一问题,提出了一种基于GPU的轴心子图同构算法.首先,通过一种新...     

应用层组播的最小延迟生成树算法

实时传输是应用层组播技术的一个主要应用领域,对网络延迟有严格的限制.保证低延迟组播成功的关键在于构建高效的应用层组播树,研究构建最小延迟应用层组播树的算法.首先分析影响延迟的3个因素:链路的传输时间、结点的发送/转发时间和结点度,然后把求解应用层组播树的问题抽象成对边和点都带权的有向图求解"度约束最小延迟生成树"的问题,同时证明这个问题属于NP-hard,并且提出了两类启发式近似算法:基于度的算法和基于最大延迟路径的算法.最后通过模拟实验说明了所提出算法的有效性.     

内部节点受限的最小生成树问题算法研究

研究内部节点受限的最小生成树问题：给定一个赋权无向完全图[G=V,E],假定[w:E→R+]为边集[E]的权重函数且满足三角不等式,给定点集[V]的一个子集[RR?V],目标是寻找图[G]的一个满足[R]中的点皆为内部顶点的权重最小的生成树。由于该问题是[NP-]困难的,提出了一个伪多项式时间最优算法,设计了一个近似比为2的多项式时间近似算法,并且给出例子以说明该近似比是紧的。     

A new neural network algorithm for planarization problems

To deal with the planarization problem widely used in many applications including routing very-large-scale integration （VLSI） circuits, this paper points out that only when its vertices are arranged in some specific order in a line can a planar graph be embedded on a line without any cross connections or cross edges. Energy function is proposed to meet the need of embedding a graph on a single line and route it correctly. A Hopfield network is designed according to the proposed energy function for such embedding and routing. The advantage of the proposed method is that it not only can detect if a graph is a planar one or not, but also can embed a planar graph or the maximal planar subgraph of a non-planar graph on a single line. In addition, simulated annealing is employed for helping the network to escape from local minima during the running of the Hopfield network. Experiments of the proposed method and its comparison with some existent conventional methods were performed and the results indicate that the proposed method is of great feasibility and effectiveness especially for the planarization problem of large graphs.     

Finding the differential characteristics of block ciphers with neural networks

We have developed a model to represent the differential operation of block ciphers in order to help finding differential characteristics. Through this model, the whole space of differential characteristics for a block cipher is represented by a multi-level weighted directed graph. In this way, the problem of finding the best differential characteristic for a block cipher reduces to the problem of finding the minimum-weight multi-branch path between two known nodes in the proposed graph. In this paper, we use recurrent neural networks to find such a path in the differential operation graph of a block cipher. The path is found through minimization of the network cost function. We use the Hopfield network and the Boltzmann machine with and without chaos to minimize the cost function. Chaos is introduced to assist the network to escape from the local minima of the cost function. Experimental results indicate the usefulness of the approach and comparison of the performance of the used techniques shows that the Boltzmann machine algorithm incorporating simulated annealing produces the best result.     

Hierarchical Multilabel Classification with Optimal Path Prediction

We consider multilabel classification problems where the labels are arranged hierarchically in a tree or directed acyclic graph (DAG). In this context, it is of much interest to select a well-connected subset of nodes which best preserve the label dependencies according to the learned models. Top-down or bottom-up procedures for labelling the nodes in the hierarchy have recently been proposed, but they rely largely on pairwise interactions, thus susceptible to get stuck in local optima. In this paper, we remedy this problem by directly finding a small number of label paths that can cover the desired subgraph in a tree/DAG. To estimate the high-dimensional label vector, we adopt the advantages of partial least squares techniques which perform simultaneous projections of the feature and label space, while constructing sound linear models between them. We then show that the optimal label prediction problem with hierarchy constraints can be reasonably transformed into the optimal path prediction problem with the structured sparsity penalties. The introduction of path selection models further allows us to leverage the efficient network flow solvers with polynomial time complexity. The experimental results validate the promising performance of the proposed algorithm in comparison to the state-of-the-art algorithms on both tree- and DAG-structured data sets.     

Treewidth computations I. Upper bounds

For more and more applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast.This paper gives an overview of several upper bound heuristics that have been proposed and tested for the problem of determining the treewidth of a graph and finding tree decompositions. Each of the heuristics produces tree decompositions whose width may be larger than the optimal width. However, experiments show that in many cases, the heuristics give tree decompositions whose width is close to the exact treewidth of the input graphs.     

Multicast communication in multicomputer networks

Efficient routing of messages is a key to the performance of multicomputers. Multicast communication refers to the delivery of the same message from a source node to an arbitrary number of destination nodes. While multicast communication is highly demanded in many applications, most of the existing multicomputers do not directly support this service; rather it is indirectly supported by multiple one-to-one or broadcast communications, which result in more network traffic and a waste of system resources. The authors study routing evaluation criteria for multicast communication under different switching technologies. Multicast communication in multicomputers is formulated as a graph theoretical problem. Depending on the evaluation criteria and switching technologies, they study three optimal multicast communication problems, which are equivalent to the finding of the following three subgraphs: optimal multicast path, optimal multicast cycle, and minimal Steiner tree, where the interconnection of a multicomputer defines a host graph. They show that all these optimization problems are NP-complete for the popular 2D-mesh and hypercube host graphs. Heuristic multicast algorithms for these routing problems are proposed     

Object recognition and articulated object learning by accumulative Hopfield matching

In this paper, a novel object recognition method based on attributed relational graph matching is proposed, which is called accumulative Hopfield matching. We first divide the scene graph into many sub-graphs, and a modified Hopfield network is then constructed to obtain the sub-graph isomorphism between each sub-scene graph and model graph. The final result is deduced by accumulating the solutions of all small sub-networks. Comparing to the traditional Hopfield network, the proposed system has the advantage of finding homomorphic mappings between two graphs. Furthermore, the system can be applied for articulated object recognition and visual model learning, which is considered as a difficult topic till now. The proposed method has been evaluated with real images.     

Query Optimization in Multidatabase Systems

Global query execution in a multidatabase system can be done parallelly, as all the local databases are independent. In this paper, a cost model that considers parallel execution of subqueries for a global query is developed. In order to obtain maximum parallelism in query execution, it is required to find a query execution plan that is represented in the form of a bushy tree and this query tree should be balanced to the maximal possible extent with respect to execution time. A new bottom up approach called Agglomerative Approach (AA) is proposed to construct balanced bushy trees with respect to execution time. By the deterministic nature of this approach, it generates local optimal solutions. This local minima problem will be severe in the case of graph queries, i.e., queries that are represented with a graph structure. A Simulated annealing Approach (SA) is employed to obtain a (near) optimal solution. These approaches (AA and SA) are suitable for handling on-line and off-line queries respectively. A Hybrid Approach (HA), that is an integration of AA and SA, is proposed to optimize queries for which the estimated time to be spent on optimization is known a priori. Results obtained with AA and SA on both tree and graph structured queries are presented.     

Degree constrained minimum spanning tree problem: a learning automata approach

Degree-constrained minimum spanning tree problem is an NP-hard bicriteria combinatorial optimization problem seeking for the minimum weight spanning tree subject to an additional degree constraint on graph vertices. Due to the NP-hardness of the problem, heuristics are more promising approaches to find a near optimal solution in a reasonable time. This paper proposes a decentralized learning automata-based heuristic called LACT for approximating the DCMST problem. LACT is an iterative algorithm, and at each iteration a degree-constrained spanning tree is randomly constructed. Each vertex selects one of its incident edges and rewards it if its weight is not greater than the minimum weight seen so far and penalizes it otherwise. Therefore, the vertices learn how to locally connect them to the degree-constrained spanning tree through the minimum weight edge subject to the degree constraint. Based on the martingale theorem, the convergence of the proposed algorithm to the optimal solution is proved. Several simulation experiments are performed to examine the performance of the proposed algorithm on well-known Euclidean and non-Euclidean hard-to-solve problem instances. The obtained results are compared with those of best-known algorithms in terms of the solution quality and running time. From the results, it is observed that the proposed algorithm significantly outperforms the existing method.     

Optimizing large join queries using a graph-based approach

Although many query tree optimization strategies have been proposed in the literature, there still is a lack of a formal and complete representation of all possible permutations of query operations (i.e., execution plans) in a uniform manner. A graph-theoretic approach presented in the paper provides a sound mathematical basis for representing a query and searching for an execution plan. In this graph model, a node represents an operation and a directed edge between two nodes indicates the older of executing these two operations in an execution plan. Each node is associated with a weight and so is an edge. The weight is an expression containing optimization required parameters, such as relation size, tuple size, join selectivity factors. All possible execution plans are representable in this graph and each spanning tree of the graph becomes an execution plan. It is a general model which can be used in the optimizer of a DBMS for internal query representation. On the basis of this model, we devise an algorithm that finds a near optimal execution plan using only polynomial time. The algorithm is compared with a few other popular optimization methods. Experiments show that the proposed algorithm is superior to the others under most circumstances     

Efficient Multimedia Distribution in Source Constraint Networks

In recent years, the number of peer-to-peer (P2P) applications has increased significantly. One important problem in many P2P applications is how to efficiently disseminate data from a single source to multiple receivers on the Internet. A successful model used for analyzing this problem is a graph consisting of nodes and edges, with a capacity assigned to each edge. In some situations however, it is inconvenient to use this model. To that end, we propose to study the problem of efficient data dissemination in a source constraint network. A source constraint network is modeled as a graph in which, the capacity is associated with a node, rather than an edge. The contributions of this paper include (a) a quantitative data dissemination in any source constraint network, (b) a set of topologies suitable for data dissemination in P2P networks, and (c) an architecture and implementation of a P2P system based on the proposed optimal topologies. We will present the experimental results of our P2P system deployed on PlanetLab nodes demonstrating that our approach achieves near optimal throughput while providing scalability, low delay and bandwidth fairness among peers.     

基于最优传输的层次化图核

已有的图核大多关注图的局部属性,利用局部的拓扑特征构建图的相似性度量,忽略图的层次结构信息.为了解决这个问题,文中提出基于最优传输的层次化图核.首先,将每个图表示成层次化的图结构.在层次化图结构构建过程中,利用K-means聚类算法构造每层图的节点,节点间的概率连接作为图的边.然后,利用带有熵约束的最优传输计算两图的层次结构上每层图之间的最优传输距离.最后,基于最优传输距离计算基于最优传输的层次化图核.在6个真实图数据集上的实验表明,文中方法可提升分类性能.     

A Hopfield network learning method for bipartite subgraph problem

We present a gradient ascent learning method of the Hopfield neural network for bipartite subgraph problem. The method is intended to provide a near-optimum parallel algorithm for solving the bipartite subgraph problem. To do this we use the Hopfield neural network to get a near-maximum bipartite subgraph, and increase the energy by modifying weights in a gradient ascent direction of the energy to help the network escape from the state of the near-maximum bipartite subgraph to the state of the maximum bipartite subgraph or better one. A large number of instances are simulated to verify the proposed method with the simulation results showing that the solution quality is superior to that of best existing parallel algorithm. We also test the learning method on total coloring problem. The simulation results show that our method finds optimal solution in every test graph.     

Conversion of the Steiner Problem on the Euclidean Plane to the Steiner Problem on Graph

If in the Steiner problem on graph the number of terminal nodes is much smaller than that of all graph nodes (say 50 against 1000), then one can see in its solution (the minimum tree) a system of paths on the graph connecting the terminal vertices, rather than a collection of separate edges (or arcs). This path system is similar to the system of segments making up the Steiner tree on the Euclidean plane: the local degree of the terminal nodes usually is 1, and the local degree of some nodes making up the paths is 3 or more. These nodes are the counterparts of the Steiner points in the problem on plane. Structural similarity of the trees in the Steiner problems on the Euclidean plane and on graph enables one to construct the algorithm to solve the Steiner problem on graph along the same lines as in the Steiner problem on the Euclidean plane. On the other hand, the solution of a problem on graph may be regarded as that on the Euclidean plane, provided that the graph satisfies certain requirements.     

Optimal distributed linear averaging

A new optimal distributed linear averaging (ODLA) problem is presented in this paper. This problem is motivated by the distributed averaging problem which arises in the context of distributed algorithms in computer science and coordination of groups of autonomous agents in engineering. The aim of the ODLA problem is to compute the average of the initial values at nodes of a graph through an optimal distributed algorithm in which the nodes in the graph can only communicate with their neighbors. Optimality is given by a minimization problem of a quadratic cost functional under infinite horizon. We show that this problem has a very close relationship with the notion of semistability. By developing new necessary and sufficient conditions for semistability of linear discrete-time systems, we convert the proposed ODLA problem into an equivalent, constrained optimization problem and then derive a solvable, fixed-structure convex optimization problem.